In the context of copyright, when the publishing rights for a book return to the author after previously having been assigned to a publisher.
In traditional publishing, the publishing rights to a book often revert to the author once the book is out of print. (Sometimes the author must also make a formal request.)
The reversion of rights is triggered by a clause in a publishing contract. The contract must contain such a clause, and the conditions must be met, otherwise the reversion of rights will not occur.
In some cases, an author whose rights have reverted to them will independently publish a new edition of the book, possibly becoming a hybrid author in the process.
In independent publishing, there is no such concept as reversion of rights, because publishing rights are typically licensed, not assigned.
Also see: traditional publishing, out of print, assign, hybrid author.